初一数学题,急在线等已知abc=1,则1+a+ab分之a + 1+b+bc分之b + 1+c+ca分之c
2019-05-29
初一数学题,急在线等
已知abc=1,则1+a+ab分之a + 1+b+bc分之b + 1+c+ca分之c
优质解答
1/(ab+a+1)+1/(bc+b+1)+1/(ac+c+1)
=abc/(ab+a+abc)+1/(bc+b+1)+1/(ac+c+1)······第一项的分子分母的1用abc代替；
=bc/(b+1+bc)+1/(bc+b+1)+1/(ac+c+1)
=(bc+1)/(bc+b+1)+1/(ac+c+1)
=(bc+abc)/(bc+b+abc)+1/(ac+c+1))······第一项的分子分母的1用abc代替；
=(c+ac)/(c+1+ac)+1/(ac+c+1)
=(ac+c+1)/(ac+c+1)
=1
1/(ab+a+1)+1/(bc+b+1)+1/(ac+c+1)
=abc/(ab+a+abc)+1/(bc+b+1)+1/(ac+c+1)······第一项的分子分母的1用abc代替；
=bc/(b+1+bc)+1/(bc+b+1)+1/(ac+c+1)
=(bc+1)/(bc+b+1)+1/(ac+c+1)
=(bc+abc)/(bc+b+abc)+1/(ac+c+1))······第一项的分子分母的1用abc代替；
=(c+ac)/(c+1+ac)+1/(ac+c+1)
=(ac+c+1)/(ac+c+1)
=1